The Argentinian is on loan from fellow Championship side Norwich City for the remainder of the year and has scored twice in five appearances since his move to south Yorkshire.
Becchio had been in line to feature against former club Leeds United on Friday at the New York Stadium, but now faces a lengthy injury lay-off after he was hurt in a behind-closed-doors friendly.
Evans confirmed Rotherham and Norwich will be in discussions regarding the 30-year-old's rehabilitation.
"Regretfully the player will be out injured for at least six weeks with a fractured heel," Evans told the club's official website.
"The player picked up this injury in a behind-closed-doors match, at a point when no player was near him and he twisted to make a run in the opposite direction.
"The player was x-rayed straight after the match, which showed no damage, but a further scan on Friday morning diagnosed the hairline fracture.
"Our dialogue with Norwich City in relation to the player will continue to ensure we get the player back playing at the earliest opportunity."
‘The pure simplicity of the way Slot has managed the squad is probably the biggest thing I could say about him. It’s not broken, so let’s get on with it’: Liverpool legend full of admiration for Jurgen Klopp's successor at Anfield
‘I trained at Spurs and thought they’d give me a chance. But I received a letter thanking me but saying they didn’t think I was good enough – I was gutted’: How Tottenham missed out on signing Wales legend John Toshack
